Calculation of the Self-Broadening of Raman Lines due to Dipolar and Quadrupolar Forces

The impact theory of Raman line broadening due to anisotropic intermolecular forces, developed previously, is applied to the broadening due to dipolar and quadrupolar forces. The optical cross sections are calculated assuming the isotropic intermolecular potential to be a hard-sphere potential, and neglecting the spread in velocities. Explicit expressions are derived for the phase-shift contribution to the width of the isotropic (j = 0) and anisotropic (j = 2) Raman scattered light as a function of the rotational quantum number J. For j = 2 scattering the phase shifts produced in the radiation do not vanish when the initial and final states of the radiation process are identical, and the phase-shift contribution to the width of the anisotropic components of the Q lines is of the same order of magnitude as for the S lines. In all cases the phase-shift contribution tends to zero when J becomes large compared with j. The contribution to the width of the inelastic collisions also tends to zero for large J, bu...